Question

In arithmetic progression the difference between the 8th and 4th term is 20 and the 8th term is ½ times the 4th term. Find the common difference and the first term in the sequence

Answer 1

So what do you think is the awnser

Answer 2

I don't know

Answer 3

I can help you but I cant give you a direct awnser

Answer 4

But if anyone knows please show how you solved it

Answer 5

OK

Answer 6

I cant help you that well but I can try my best

Answer 7

OK no problem

Answer 8

OK thanks a lot❤

Answer 9

No prob

Answer 10

do you need any more help

Answer 11

No for now

Answer 12

Ok just tell me if you need any more help

Answer 13

Do you have any other method

Answer 14

Like using simultaneous or elimination method

Answer 15

generic arithmetic sequence formula
\[a_{n}=a_{1}+(n-1)d\]

for the 4th and 8 terms:
\[a_{8}=a_{1}+(8-1)d\]\[a_{4}=a_{1}+(4-1)d\]

it says "the difference between the two terms is 20" so we can subtract a8 - a4 to get

a8 - a4 = (8-1)d - (4-1)d = 20

solve for d to get the common difference

"8th term is ½ times the 4th term"
so a8 = (1/4)a4

you can plug (1/4)a4 into the a8 equation to get
\[(1/4)a_{4}=a_{1}+(8-1)d\]
you can multiply this by 4 on both sides to get
a4 = 4(a1 + (8-1)d)
now, looking at the original a4 equation\[a_{4}=a_{1}+(4-1)d\]
you can set these a4 equations equal to each other, plug in the d-value from before, and solve for a1